Reference technology sets, Free Disposal Hulls and productivity decompositions

•Productivity growth is decomposed into explanatory factors.•Relative unrestrictive regularity conditions are used.•Specification of the relevant reference technologies is addressed.•Context is a panel of production units and Free Disposal Hull methods.

Diewert and Fox (2013) proposed decompositions of a Malmquist-type productivity index into explanatory factors, with a focus on extracting technical progress, technical efficiency change and returns to scale components. A major problem with their decompositions is that it may be difficult to determine the appropriate reference technologies. Using relatively unrestrictive regularity conditions, the paper develops a data envelopment type approach for decomposing productivity growth for a panel of production units into explanatory factors based on the Free Disposal Hull methods pioneered by Tulkens and his co-authors.